Vargas scored a goal in each half, while a Gary Medal own-goal on the hour mark gave Peru a lifeline.
Not for the first time, the hosts saw their opposition lose a player in controversial circumstances. Carlos Zambrano was shown a straight red card in the 21st minute after his follow through from a clearance caught Charles Aranguiz on the waist. While the defender's studs were up, there did not appear to be much malice or intent in the incident.
Referee Jose Argote had his hands full early on after a clash between Zambrano and Arturo Vidal, with the Chile striker lucky not to see a card of any nature after putting his hands in Zambrano's face.
Peru had the better of the early chances, with Jefferson Farfan's header hitting the post after nine minutes before Carlos Lobaton found the side netting.
However, the match turned in Chile's favour when Zambrano was giving his marching orders for catching Aranguiz.
Chile began to take the ascendancy, and Jorge Valdivia come close on the half-hour mark when his curling effort went just wide of the post.
Vargas would make no mistake with just two minutes remaining in the half, with the Napoli striker on hand to tap-in after Alexis Sanchez's cross rebounded off the post.
The Chilean striker had the ball in the back of the net once more in the 61st minute, only to see his effort incorrectly ruled out for offside as the officials' bad night in Santiago continued.
Farfan has a chance to draw Peru level in the 58th minute, but he could not make clean contact with Luis Advincula's quality delivery, with the ball coming off his shoulder on it's way to Chile keeper Claudio Bravo.
Peru had their goal just two minutes later though, and again it was a great ball from Advincula that caused the problems. Medel failed to deal with the right-back's whipped-in ball and could only divert it into the back of his own net.
The equaliser was no less than what Peru deserved, but they would not remain level for long. Vargas scored what would be the decisive goal in fine fashion on 64 minutes, with the striker unleashing a stunning dipping strike from 30-yards out that left Pedro Gallese with no chance.
Rather than sit back and protect their advantage, Chile looked for the third goal that would kill the game off, and Sanchez nearly found it with ten minutes to play, but he fired over from inside the area.
Peru would not go down without a fight, and Paolo Guerrero thought he should have had a penalty late on after tangling with Jose Rojas, but his appeals where waved away.
Chile held on to claim the victory, and with it their first Copa America final in 28 years, while for Peru the dream is over. However, Ricardo Gareca's side can take much heart from a performance that suggested they are worthy of a much higher ranking than the 61st place they currently occupy.
Chile will now face either Argentina or Paraguay in the final.